Seasonally-Adjusted Data: What it Really Means

This paper provides a brief overview of what it means when data are seasonally-adjusted and describes the advantages of using seasonally adjusted data to examine changes in data. The Bureau of Transportation Statistics’ airline data are used as an illustrative example.

Statisticians use the process of seasonal-adjustment to uncover trends in data. Monthly data, for instance, are influenced by the number of days and the number of weekends in a month as well as by the timing of holidays and seasonal activity. These influences make it difficult to see underlying changes in the data. Statisticians use seasonal adjustment to control for these influences.

Controlling of seasonal influences allows measurement of real monthly changes; short and long term patterns of growth or decline; and turning points. Data for one month can be compared to data for any other month in the series and the data series can be ranked to find high and low points. Any observed differences are “real” differences; that is, they are differences brought about by changes in the data and not brought about by a change in the number of days or weekends in the month, the occurrence or non-occurrence of a holiday, or seasonal activity.

Seasonal adjustment is used for many time-series such data sets as the Bureau of Economic Analysis’ quarterly Gross Domestic Product (GDP), the Census Bureau’s U.S. International Trade in Goods and Services, New Residential Sales and New Residential Construction, and the Bureau of Labor Statistics’ monthly Employment Situation Summary.

Transportation data tend to be highly seasonal. Revenue passenger-miles (RPMs), a measure of air travel demand, are strongly affected by seasonal activity. RPMs tend be to higher in summer months because of vacation-related travel and tend to rise in the month containing Easter, which changes year-to-year. These are normal, intra-yearly (seasonal) changes, which can be modeled so as to uncover underlying changes in the data itself – for instance, changes in RPMs after 9/11.

RPMs viewed over a 14-year period illustrate the differences between unadjusted and seasonally-adjusted data. Between January 2000 and January 2014, unadjusted RPMs were the highest in July 2013, followed by three other Julys. After seasonal adjustment, those Julys rank significantly lower, as the seasonal adjustment process controls for seasonal movement in travel. The seasonally-adjusted data show that all of the top five months between January 2000 and January 2014 took place in the months of November through January and the top month was January 2014, followed by the months of December and November 2013. (See Table 1)

Available seat-miles (ASMs), a measure of airline capacity, also illustrate the differences between unadjusted and seasonally-adjusted data. ASMs are highly seasonal and as a result, it is difficult to discern trends in ASMs without seasonal adjustment. The seasonally-adjusted numbers show that no month since May 2008 has broken into the top 10 months for capacity. Airlines reduced capacity in 2008 in response to the recession and to the increase in the cost of fuel; airlines have not yet returned to capacity levels operated before these events. Unadjusted numbers suggest otherwise; they show that airlines operated at highest capacity in July 2013. That month, however, ranks lower after seasonal adjustment, because of the control for the natural increase of airline passenger travel in July. (See Table 2)

TABLE 2. MONTHS WITH THE HIGHEST AVAILABLE SEAT MILES (ASMS) (TOP 10)

(Jan. 2000 – Jan. 2014)

Ranked by Unadjusted ASMs (thousands)

Rank (unadjusted)

Date

Unadjusted

Adjusted

Rank (adjusted)

1

July-2013

93,812,376

84,551,333

28

2

July-2008

93,730,360

85,809,078

15

3

July-2007

92,900,560

85,672,566

17

5

July-2011

92,505,512

83,345,640

52

6

August-2013

92,159,056

84,870,242

24

7

July-2012

91,937,384

82,707,051

76

8

August-2008

91,768,768

84,943,658

21

9

July-2005

90,483,560

84,390,298

33

10

July-2006

90,151,120

83,563,082

48

Ranked by Seasonally-adjusted ASMs (thousands)

Rank (adjusted)

Date

Adjusted

Unadjusted

Rank (unadjusted)

1

November-2007

88,323,472

83,926,904

56

2

December-2007

88,107,858

87,368,016

28

3

January-2008

88,006,180

85,823,992

38

5

October-2007

87,709,527

86,936,672

31

6

March-2008

87,484,395

89,259,056

17

7

September-2007

87,059,611

84,375,736

52

8

May-2008

86,784,781

88,697,896

20

9

April-2008

86,626,984

85,702,944

40

10

January-2007

86,355,182

84,354,432

53

NOTES: Available seat miles from all U.S. air carrier domestic and international, scheduled passenger flights

SEASONAL ADJUSTMENT IN TRANSPORTATION

Seasonal adjustment is the process of estimating and removing movement in a time-series caused by regular seasonal variation in activity, e.g., an increase in air travel during summer months. Calendar effects (trading days and holidays) often introduce additional movement in the time-series, and data outliers may disrupt movement altogether. Both calendar effects and data outliers make it difficult to uncover regular seasonal movement. Statisticians therefore control for the effects of both, when necessary, in seasonally-adjusting a time-series.

Calendar Effects: Trading Days and Holidays

There are two types of calendar effects that introduce year-to-year variation in seasonal movements. The first is trading day effects. Trading day effects result from the differences in the number of days in the month across months and the number of times each day of the week occurs in the month between years. For instance, January 2014 contains five Fridays while January 2013 contains only four. Trading day effects do not impact all time-series; they tend to impact time-series where there is significant variation in activity by day of week. Statisticians use statistical tests to determine whether trading day effects impact a time-series. Neither RPMs or ASMs are impacted by trading day effects.

The second type of calendar effect results from holidays occurring on different days of the month (e.g., Labor Day and Thanksgiving) and from holidays moving between months across years (e.g., Easter). Holidays generate holiday-related activity, such as an increase in travel or retail sales, before and/or after the holiday itself. When a holiday is close to the beginning or end of the month, holiday-related activity may occur, respectively, in the month before or the month after the actual month containing the holiday. For instance, post-Thanksgiving travel may occur in December when the Thanksgiving holiday occurs close to the end of November. The spilling over of holiday-related activity into another month can be problematic when a holiday, such as Thanksgiving, occurs on a different day of the month across years. If the holiday occurred on a fixed date, then the amount of spilling over would be constant year to year. When a holiday occurs on a fixed day of the week rather than a fixed date, the amount of spilling over may be larger in some years than others. This may introduce non-seasonal movement into the time series; the month into which holiday-related travel spilled may have a data value larger than expected.

In some cases, there may be no impact. This happens when the holiday-related activity does not carry over into the month before or after or when the holiday-related activity that carries over is not large enough to significantly change the expected amount of activity for that month. When significant, the holiday must be controlled for during seasonal adjustment. Statisticians use statistical tests to determine whether significant. The model used by the Bureau of Transportation Statistics (BTS) to seasonally adjust airline RPMs controls for Thanksgiving as Thanksgiving was found to significantly impact RPMs in December when Thanksgiving occurred late in November and holiday-related activity resultantly carried over into December.

Holidays that move across months also may cause holiday-related activity to spill-over into the month before or after the holiday itself. They additionally cause a change in the timing for all, or a majority, of holiday-related activity. Holiday related travel, for instance, associated with Easter may fall entirely within March in one year and in April in the next when the Easter holiday moves to April. In some years, Easter may fall at the end of March and as a result, Easter-related travel may spill over into April. For example, Easter took place in April in 2007 but in March in 2008. The BTS seasonal-adjustment model places all Easter-related travel, in 2007, in April and in 2008, in March. Unadjusted RPMs rose 2.7 percent from March 2007 to 2008; the seasonally-adjusted numbers, which account for Easter-related travel occurring wholly in March 2008 and not at all in March 2007, show an increase of only 1.3 percent (see table 4). Easter was not found to significantly impact ASMs.

Data Outliers

Data outliers disrupt seasonal movements by injecting additional variation, or noise, into the data. They typically introduce intra-yearly disruptions in regular movements in the data. Intra-yearly disruption may occur when an unexpected event happens, such as 9/11 which reduced the number of RPMs below what would be expected from regular seasonal movement alone for the data collection period. Seasonally-adjusted RPMs, for example, declined 28.4 percent in September 2001 from the previous September as a result of 9/11. The disruption caused by events may extend beyond the time period in which they occur. Events such as 9/11 tend to cause more lasting disruptions; they may cause an overall decline or increase that persists beyond the data collection period in which they occurred; in other words, they change the overall level of the data series. For instance, RPMs fell overall after 9/11 and did not rise above their pre-9/11 level until April 2004, when looking at seasonally-adjusted numbers. All data outliers – those that change the level of a time-series and those that disrupt the expected movement in the collection period in which they occur - must be estimated and controlled for prior to seasonal adjustment. Their presence makes it difficult to create a model that removes seasonal effects as the seasonal effects cannot otherwise be isolated from the effects of data outliers.

Seasonal Effects

Seasonal adjustment removes seasonal effects. The seasonal effect in a time-series is any effect that is reasonably stable in terms of annual timing, direction, and magnitude. This includes changes brought about by the seasons themselves, such as increases in passenger air travel during summer months when vacation rates tend to be higher. Removal of seasonal effects after controlling for the effects from trading days, moving holidays, and data outliers makes estimating changes due to factors other than calendar effects, data anomalies, and seasonality, such as a change in air travel resulting from economic conditions, more accurate. Inaccurate pictures of underlying changes are more likely when data are highly seasonal. For example, the decline in ASMs during the 2007 to 2009 recession cannot be seen as easily or measured accurately when looking at unadjusted data. Unadjusted ASMs in July 2009 (the first month after the recession) exceeded those in November 2007 (the month prior to the start of the recession). The adjusted data provides a more accurate picture of the impact of the recession because it controls for seasonal effects. The natural increase of ASMs in July, induced by vacation-related travel, makes it look like ASMs rebounded immediately after the end of the recession. This is not the case; seasonally-adjusted ASMs have not re-bounded since the recession (see figure 1).

FIGURE 1. AVAILABLE SEAT MILES (ASMS), JANUARY 2000 TO JANUARY 2014

NOTES: Available seat miles from all U.S. air carrier domestic and international, scheduled passenger flights

Applying seasonal adjustment to BTS airline data illustrates its usefulness. The following more detailed example shows how seasonal adjustment can be used to look at real changes in RPMs. The adjusted and unadjusted data used in the following example can be found here.

Seasonally-adjusted data help uncover short and long-term trends in RPMs. Short and long-term trends in the airline industry traditionally have been depicted by year-over-year changes in unadjusted data. These comparisons skirt around the influence of seasonal movements by comparing the same month (e.g., May to May) but are flawed for two reasons. First, the months may be disparate because of calendar effects, e.g., one may contain Easter while the other does not. Second, variation may occur between the months; there may be an overall rise (decline) between the months but some decline (growth) within. For instance, RPMs rose between May 2012 and May 2013 but did not climb steadily. This is difficult to see when looking at unadjusted numbers because of seasonal movement (e.g., RPMs rising naturally in the summer as vacation-related travel rises). When seasonally-adjusted, it can be seen that RPMs rose but not steadily from May 2012 and declined between February and March, only rising once again in May just above the February 2012 number (see table 3).

TABLE 3. REVENUE PASSENGER MILES (RPMS), MAY 2012-MAY 2013

(Thousands)

Date

Unadjusted

Seasonally-adjusted

Value

Percent change

Value

Percent change

May-2012

71,155,609

68,360,655

June-2012

76,014,162

6.8

68,491,139

0.2

July-2012

79,640,786

4.8

68,140,804

-0.5

August-2012

77,738,861

-2.4

68,705,504

0.8

September-2012

65,230,938

-16.1

68,477,562

-0.3

October-2012

66,974,008

2.7

68,311,549

-0.2

November-2012

63,372,211

-5.4

68,800,874

0.7

December-2012

65,923,928

4

68,809,269

0

January-2013

62,433,152

-5.3

69,357,012

0.8

February-2013

57,526,035

-7.9

70,010,282

0.9

March-2013

72,164,049

25.4

69,375,821

-0.9

April-2013

67,827,663

-6

69,587,244

0.3

May-2013

72,980,842

7.6

70,067,688

0.7

Year-over-year change

2.6

2.5

NOTES: Revenue passenger miles from all U.S. air carrier domestic and international, scheduled passenger flights

Seasonal adjustment controls for calendar effects and data outliers and removes seasonal effects. The model developed by BTS to seasonally adjust RPMs detects and controls for calendar effects and outliers present in the data before seasonally adjusting the data. Looking at year-over-year changes in the unadjusted and adjusted data show how inaccurate pictures may be drawn from the unadjusted data; there are significant differences in the estimated changes. This can be seen clearly in making year-over-year comparisons for the month of March, as an example. RPMs tend to increase in March when Easter occurs in that month. Easter, however, may occur in March in one year and April in the following year. Thus, year-over-year comparisons of revenue passenger miles for March are misleading when the effect of Easter is not taken into account. Easter is a holiday that was found by BTS to significantly influence RPMs and is controlled for in the model used to seasonally adjust RPMs.

Table 4 shows the year-over-year change in RPMs for the unadjusted and adjusted series for the month of March from 2000 to 2013. Year-over-year changes in unadjusted RPMs are noticeably different from the adjusted values when a March without an Easter occurrence is compared to one with (these values are bolded in Table 1). The difference is most noticeable in comparing March 2004 with March 2005. The unadjusted data suggests RPMs increased 11.0 percent from March 2004 to March 2005. This increase is due, partially, to the occurrence of Easter in March 2005 which spurred holiday-related travel and thereby boosted RPMs above the March 2004 level, which was unaffected by Easter related travel. If Easter is taken into account, as in the seasonally-adjusted data, the increase is only 8.7 percent: 2.3 percentage points lower than the value calculated from the unadjusted data.

TABLE 4. UNADJUSTED AND SEASONALLY-ADJUSTED REVENUE PASSENGER MILES FOR THE MONTH OF MARCH, 2000-2013

Begin date of Easter travel

Easter date(1)

End date of Easter travel

Thousands

Year-over-year percent change

Percent-age point difference

Unadjusted

Seasonally- Adjusted

Unadjusted

Seasonally- Adjusted

2000

NA

NA

NA

59,632,015

56,801,077

2001

NA

NA

NA

60,769,074

58,100,149

1.9

2.3

0.4

2002

3/28/2002

3/31/2002

4/2/2002

56,037,382

52,708,478

-7.8

-9.3

1.5

2003

NA

NA

NA

54,994,261

52,763,526

-1.9

0.1

-1.8

2004

NA

NA

NA

61,923,381

59,610,118

12.6

13.0

0.4

2005

3/24/2005

3/27/2005

3/29/2005

68,725,711

64,789,311

11.0

8.7

-2.3

2006

NA

NA

NA

69,483,899

66,708,174

1.1

3.0

1.9

2007

NA

NA

NA

71,497,177

68,851,912

2.9

3.2

0.3

2008

3/20/2008

3/23/2008

3/25/2008

73,427,185

69,746,721

2.7

1.3

-1.4

2009

NA

NA

NA

65,147,741

63,222,826

-11.3

-9.4

-1.9

2010

NA

NA

NA

67,304,853

65,469,595

3.3

3.6

0.2

2011

NA

NA

NA

69,104,312

67,294,729

2.7

2.8

0.1

2012

NA

NA

NA

70,799,480

68,884,609

2.5

2.4

-0.1

2013

3/28/2002

3/31/2013

4/2/2013

72,164,049

69,375,821

1.9

0.7

-1.2

(1) NA where Easter holiday does not occur in the month of March

NOTES: Revenue passenger miles from all U.S. air carrier domestic and international, scheduled passenger flights

Holiday effects are not necessarily isolated to a single month when looking at transportation data. Travel tends to increase before and after the holiday and not just on the holiday itself. When a holiday occurs towards the beginning or end of a month, increases in travel may be observed in the month prior or the month after, respectively. This creates an additional problem in making year-over-year comparisons in the presence of a moving holiday like Easter. Years where the holiday is present in neither month may be affected by these spillover effects – that is data values may be higher because of pre- or post-holiday travel induced by the holiday occurring in the next or previous month, respectively.

In developing the model to seasonally adjust revenue passenger miles, BTS found a significant increase in passenger air travel the three days prior to through the two days after Easter1. When Easter occurs late in March, as in 2002 and 2013, travel induced by the Easter holiday spills over into April (see Table 4). Without adjustment, there is a 1.9 percent rise in RPMs from March 2012 to March 2013. Using seasonal adjustment to account for the holiday, the increase drops to 0.7 percent.

There is no spill-over effect in the years from 2000 to 2013 from Easter occurring in April because the entire Easter holiday travel period took place in the month of April without spilling over into March or May. Unadjusted data for the month of April, however, cannot be accurately compared across years because not all Aprils contain Easter and because some (April 2002 and 2013) are affected by Easter-related travel spilling over from March into April.

Year-over-year comparisons are made more accurate when using seasonally-adjusted data because seasonal adjustment controls for calendar effects and data outliers. Because seasonal adjustment removes seasonal effects, data can be compared across months and years directly. This comparison can be misleading with unadjusted data. Seasonal movements in unadjusted data make it difficult even to see trends within the data. Figure 1, which shows unadjusted and seasonally-adjusted revenue passenger miles, demonstrates this. Seasonal movement causes RPMs to vary significantly within a year. RPMs tend to climb in the summer months because of vacation related travel; they then fall through the winter months, reaching a low in February. This seasonal movement makes it difficult to see RPMs are growing or declining. However, once the seasonal-adjustment process accounts for seasonal movement, data trends can be seen more readily – as in Figure 1 for RPMs – and computed across all months and years. The adjustment gives a more nuanced picture of the data than year-over-year comparisons.

FIGURE 2. REVENUE PASSENGER MILES, JANUARY 2000 TO JANUARY 2014

NOTES: Revenue passenger miles from all U.S. air carrier domestic and international, scheduled passenger flights

Seasonally-adjusted data help uncover real monthly changes; short and long term patterns of growth or decline; and turning points. Unadjusted data can be misleading when used to measure these types of underlying changes because of calendar related effects.

1 The Bureau of Transportation Statistics referred to industry experts in determining the number of days before and after a holiday when holiday traffic is expected. This was used to create a parameter in the seasonal adjustment model. Various parameters were tried until finding the most significant parameter and best fitting model.